Opuscula Mathematica
Opuscula Math. 31, no. 3 (), 411-424
Opuscula Mathematica

Existence and asymptotic behavior of solutions for Hénon type equations

Abstract. This paper is concerned with ground state solutions for the Hénon type equation \(-\Delta u(x)=|y|^{\alpha} u^{p-1}(x)\) in \(\Omega\), where \(\Omega=B^k(0,1)\times B^{n-k}(0,1)\subset \mathbb{R}^n\) and \(x=(y,z) \in \mathbb{R}^k \times \mathbb{R}^{n-k}\). We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions for the problem. We also investigate asymptotic behavior of the ground state solution when \(p\) tends to the critical exponent \(2^*=\frac {2n}{n-2}\) if \(n\geq 3\).
Keywords: Hénon equation, cylindrical symmetry, non-cylindrical symmetry, asymptotic behavior.
Mathematics Subject Classification: 35J50, 35J55, 35J60.
Cite this article as:
Wei Long, Jianfu Yang, Existence and asymptotic behavior of solutions for Hénon type equations, Opuscula Math. 31, no. 3 (2011), 411-424, http://dx.doi.org/10.7494/OpMath.2011.31.3.411
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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